README.md

295. 数据流的中位数

English Version

题目描述

中位数是有序列表中间的数。如果列表长度是偶数，中位数则是中间两个数的平均值。

例如，

[2,3,4] 的中位数是 3

[2,3] 的中位数是 (2 + 3) / 2 = 2.5

设计一个支持以下两种操作的数据结构：

• void addNum(int num) - 从数据流中添加一个整数到数据结构中。
• double findMedian() - 返回目前所有元素的中位数。

示例：

addNum(1)
addNum(2)
findMedian() -> 1.5
addNum(3)
findMedian() -> 2

进阶:

1. 如果数据流中所有整数都在 0 到 100 范围内，你将如何优化你的算法？
2. 如果数据流中 99% 的整数都在 0 到 100 范围内，你将如何优化你的算法？

解法

• 创建大根堆、小根堆，其中：大根堆存放较小的一半元素，小根堆存放较大的一半元素。
• 添加元素时，先放入小根堆，然后将小根堆对顶元素弹出并放入大根堆（使得大根堆个数多 1）；若大小根堆元素个数差超过 1，则将大根堆元素弹出放入小根堆。
• 取中位数时，若大根堆元素较多，取大根堆堆顶，否则取两堆顶元素和的平均值。

Python3

class MedianFinder:

    def __init__(self):
        """
        initialize your data structure here.
        """
        self.min_heap = []
        self.max_heap = []

    def addNum(self, num: int) -> None:
        heapq.heappush(self.min_heap, num)
        heapq.heappush(self.max_heap, -heapq.heappop(self.min_heap))
        if len(self.max_heap) - len(self.min_heap) > 1:
            heapq.heappush(self.min_heap, -heapq.heappop(self.max_heap))

    def findMedian(self) -> float:
        if len(self.max_heap) > len(self.min_heap):
            return -self.max_heap[0]
        return (self.min_heap[0] - self.max_heap[0]) / 2


# Your MedianFinder object will be instantiated and called as such:
# obj = MedianFinder()
# obj.addNum(num)
# param_2 = obj.findMedian()

Java

class MedianFinder {
    private PriorityQueue<Integer> minHeap;
    private PriorityQueue<Integer> maxHeap;

    /** initialize your data structure here. */
    public MedianFinder() {
        minHeap = new PriorityQueue<>();
        maxHeap = new PriorityQueue<>(Collections.reverseOrder());
    }

    public void addNum(int num) {
        minHeap.offer(num);
        maxHeap.offer(minHeap.poll());
        if (maxHeap.size() - minHeap.size() > 1) {
            minHeap.offer(maxHeap.poll());
        }
    }

    public double findMedian() {
        if (maxHeap.size() > minHeap.size()) {
            return maxHeap.peek();
        }
        return (minHeap.peek() + maxHeap.peek()) * 1.0 / 2;
    }
}

/**
 * Your MedianFinder object will be instantiated and called as such:
 * MedianFinder obj = new MedianFinder();
 * obj.addNum(num);
 * double param_2 = obj.findMedian();
 */

C++

class MedianFinder {
public:
    /** initialize your data structure here. */
    MedianFinder() {}

    void addNum(int num) {
        max_heap.push(num);
        min_heap.push(max_heap.top());
        max_heap.pop();
        if (min_heap.size() > max_heap.size()) {
            max_heap.push(min_heap.top());
            min_heap.pop();
        }
    }

    double findMedian() {
        if (max_heap.size() > min_heap.size()) {
            return max_heap.top();
        }
        return (double)(max_heap.top() + min_heap.top()) / 2;
    }

private:
    priority_queue<int> max_heap;
    priority_queue<int, vector<int>, greater<int>> min_heap;
};

/**
 * Your MedianFinder object will be instantiated and called as such:
 * MedianFinder* obj = new MedianFinder();
 * obj->addNum(num);
 * double param_2 = obj->findMedian();
 */

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